Scrum team one dev

Even if it's theoretically possible to implement Scrum as it's defined in the Scrum Guide for a team with a single Developer, does it make sense? Or might it be too much overhead?

When it comes to scaling frameworks for Scrum, the typical advice is to look at the formalized scaling frameworks once you have three teams since the structures for coordination become more important once you have more than two teams. I'd suggest that something similar is true for Scrum - until you have at least 2 or 3 Developers coordinating with a Product Owner and Scrum Master, I'm not sure you need the structures of Scrum. Some of the practices, individually, may be useful to incorporate so they are in place if the team grows.

I'll work on a project with one member on scrum team, just a one dev and po. How to apply scrum framework for o only one member? Is it possible?

That's 2 members. A Scrum Master would make a third.

Anyhow, a better question to ask might be, is it useful to apply Scrum here? Is a complex problem being addressed for which empiricism would prove beneficial? If so, does such a small team actually need a framework to guide them?

Consider whether Scrum is the right framework for the delivery. Is it a complex product? Scrum is lightweight but there is still a time requirement to fulfil the accountabilities as described.

There is no minimum Scrum Team size, so there is no rule being broken by having a smaller than typical size.

Scrum isn’t always the answer. You can certainly apply empirical theory which would almost certainly be a positive step.

Only you can determine whether Scrum is the best option for the delivery.